Time Series Alignment with Global Invariances
This addresses the challenge of time series alignment for applications in machine learning and signal processing, though it appears incremental as it builds on existing alignment methods with added global invariances.
The paper tackles the problem of measuring distance between multivariate time series with differing temporal dynamics and feature representations by proposing a novel distance that accounts for both feature space and temporal variabilities through joint optimization. The result shows robustness compared to state-of-the-art methods on simulated and real-world data.
Multivariate time series are ubiquitous objects in signal processing. Measuring a distance or similarity between two such objects is of prime interest in a variety of applications, including machine learning, but can be very difficult as soon as the temporal dynamics and the representation of the time series, {\em i.e.} the nature of the observed quantities, differ from one another. In this work, we propose a novel distance accounting both feature space and temporal variabilities by learning a latent global transformation of the feature space together with a temporal alignment, cast as a joint optimization problem. The versatility of our framework allows for several variants depending on the invariance class at stake. Among other contributions, we define a differentiable loss for time series and present two algorithms for the computation of time series barycenters under this new geometry. We illustrate the interest of our approach on both simulated and real world data and show the robustness of our approach compared to state-of-the-art methods.